# exploring linear and exponential growth

## exploring linear and exponential growth

In 1999, Catherine Ryan Hyde released the novel Pay It Forward. Warner Brothers turned it into a major motion picture in 2000. In the story, Trevor is in seventh grade, and he devises a plan to change the world. In Trevor’s plan, a person must repay a good deed done for them by doing a good deed for three different people. What starts as one good deed turns into three more good deeds, which grows into 3 • 3 = 9 good deeds, and so on!

Assume that the good deeds occurred each month. Look at how quickly this exponential growth can grow.

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Month

1

2

3

4

5

Good Deeds

3

9

27

81

243

What if Trevor’s plan was to perform thirty good deeds himself each month?

Month

1

2

3

4

5

Good Deeds

30

60

90

120

150

Notice that if Trevor is doing 30 good deeds each month by himself, that even though it starts looking like high numbers, it is quickly surpassed by the “pay it forward” plan. What type of functions do these plans represent?

Take a look!

The “pay it forward” plan is an exponential function, f(x) = 3x. The good deeds have a common ratio of 3.

The “Trevor do it all by himself” plan is a linear function, f(x) = 30x. The good deeds have a common difference of 30.